Whether you are buying foreclosed properties or are just buying REO properties through MLS, how do you deal with a pre-existing tenant situation? I have pulled together some legal research (see below), and it says that "the new owner takes the place of the seller and becomes the new landlord." (Section 8.7) So, if you are a new owner, and you assume the lease, you need to notify the tenant that you are the new owner and where they are to send the rental payments. The tricky questions arise if they default on the lease and they were tenants under a prior owner that lost the property in foreclosure, and the trustee's sale took place less than a year ago.
Under the "Protecting Tenants at Foreclosure Act of 2009", tenants after a foreclosure are to be given a 90-day notice to vacate before an eviction can be filed with the court. So, which is it? A 3-day notice for non-payment of rent because they defaulted on the lease, or a 90-day? As you can see from the legal research (Section 8.68F), "The scope of the Act is unclear if a tenant is in default under the Lease."
What to do? Your best bet is to establish a landlord/tenant relationship right away with the tenant by acknowledging their lease, possibly having them sign a new lease with you, and accepting rental payments. If you haven't been paid anything and no landlord/tenant relationship was ever established, your best bet is to go with a 90-day notice.